We formulate stochastic indicator parameters that characterize polluti
on levels in geographical regions with heterogeneous contaminant distr
ibutions. The indicator parameters are expressed in terms of the rando
m fields representing the contaminant distributions and the critical t
hreshold level specified by health and environmental standards. Certai
n theoretical results are proven regarding univariate and bivariate in
dicator parameters. The analytical expressions obtained are general an
d can be used in practice for various types of contaminant distributio
ns. A test of ergodicity-breaking is suggested for scientific and engi
neering applications in terms of the indicator parameters. Fractal cha
racteristics of the indicator parameters are discussed. The effects of
modelling and observation scale on exceedance contamination analysis
are examined. Indicator random field parameters are studied on both co
ntinuum and lattice domains using analytical means and numerical simul
ations.